Performance Evaluation of Decreasing Multi-State Consecutive-k-out-of-n: G Systems

Abstract

In the binary context, a consecutive-k-out-of-n: G system works if and only if at least k consecutive components are working. In the multi-state context, a consecutive-k-out-of-n: G system is in state j or above (j = 1,2,…,M) if and only if at least kl consecutive components are in state l or above for all l (1 ≤ l ≤ j). In this paper, we use minimal path vectors to evaluate the system state distribution. When M = 3, a recursive formula is provided for evaluating the system state distribution. When M ≥ 4, an algorithm is provided to bound the system state distribution. These bounds are sharper than those reported in the literature.